PQR is a right -angled triangle with ^PQR=90°
^QPR=30° and
|PQ|=50cm
find to de nearest whole namba
I.|QR|
ii.|PR|
Please translate into standard English:
find to de nearest whole namba
To find the lengths of sides QR and PR in the triangle PQR, we can use trigonometric ratios since we have the angle measures.
i. To find |QR|, we can use the sine ratio:
sin(QPR) = |QR|/|PQ|
Substituting the given values:
sin(30°) = |QR| / 50 cm
Using the sine of 30° (which is 0.5):
0.5 = |QR| / 50 cm
Simplifying the equation, we can cross multiply:
0.5 * 50 cm = |QR|
25 cm = |QR|
Therefore, |QR| is approximately 25 cm (to the nearest whole number).
ii. To find |PR|, we can use the cosine ratio:
cos(QPR) = |PR| / |PQ|
Substituting the given values:
cos(30°) = |PR| / 50 cm
Using the cosine of 30° (which is √3 / 2):
√3 / 2 = |PR| / 50 cm
Simplifying the equation, we can cross multiply:
√3 / 2 * 50 cm = |PR|
25√3 cm ≈ |PR|
Therefore, |PR| is approximately 25√3 cm (to the nearest whole number).
To find the lengths of QR and PR in the right-angled triangle PQR, we can use trigonometric ratios.
i. To find the length of QR:
We know that in a right-angled triangle, the sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. So, we can use the sine ratio to find QR.
sin(QPR) = QR / PQ
Now, substitute the given values:
sin(30°) = QR / 50 cm
Using a scientific calculator, find the sine of 30° (approximately 0.5):
0.5 = QR / 50 cm
Now, isolate QR by multiplying both sides by 50 cm:
0.5 * 50 cm = QR
25 cm = QR
Therefore, the length of QR is approximately 25 cm.
ii. To find the length of PR:
We can use the cosine ratio, which states that the cosine of an angle is equal to the length of the side adjacent to the angle divided by the length of the hypotenuse.
cos(QPR) = PR / PQ
Substituting the values:
cos(30°) = PR / 50 cm
Using a scientific calculator, find the cosine of 30° (approximately 0.866):
0.866 = PR / 50 cm
Multiply both sides by 50 cm to isolate PR:
0.866 * 50 cm = PR
43.3 cm ≈ PR
Therefore, the length of PR is approximately 43.3 cm (rounded to the nearest whole number is 43 cm).